Abstract

We combine the Leslie model and its derivatives with the classical compartmental SIRS models to build a model of transmission of infected diseases, in a population of hosts, whether opened or closed systems. We calculate the basic reproductive rate R0. Under certain conditions, when , there is a disease-free equilibrium that is locally asymptotically stable. In contrast, when , this equilibrium is unstable. Then, through an example, we show how we can define public health strategies to tackle an endemic. Finally we carry a global sensitivity analysis based on this basic reproduction rate to exhibit the most influential parameters of our model that are applied to influenza.